In her article, Warrington mentions many advantages of allowing children to figure things out on their own, such as children feeling a greater ability to exchange ideas and giving children the capacity to assign greater meaning to numeric problems by creating story problems for them, the biggest advantage put forward is the fact that children, if placed in the correct setting, "can construct knowledge about sophisticated and abstract concepts in mathematics without algorithms." In other words, children in Warrington's class were able to solve quite complex problems, such as 4 2/5 divided by 1/3, in their minds without the use of the 'invert and multiply' rule. Warrington makes the claim that because the students had been actively involved in the discovery process they were able to solve math problems faster and better than students who learn just the algorithms themselves. This ability for children to learn how to solve problems without algorithmic methods is a valuable skill for students to obtain because of the fact that it allows them to delve deeper into the world of mathematics.
The process of constructing knowledge on their own, children truly can learn many things about math. However, there are a few problems with this method of learning. The first is the fact that if a teacher doesn't know the correct way to approach this method of teaching, how can they be expected to "provide learning environments that allow children to be successful"? Another problem is that it would be difficult for a teacher to ensure that every student is learning the necessary skills to allow them to progress on to the next 'step' in the mathematical process. Math is all about utilizing past knowledge to delve deeper into mathematical solutions, so if a child doesn't understand a building block of math, they will find it difficult to advance in math. While I do see the advantages of this style of learning, I do think that it might not be as wonderful as it is a first look.
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Wow, what a first sentence. I was initially thinking that you were trying to pack all the advantages into one long sentence. :) I think, however, that you were trying to set the stage for focusing on what you considered to be the main advantage. There were probably clearer ways of doing this. With that said, I really liked your discussion of this main advantage, because you developed a rich description of what it entailed. I particularly liked the way that you paraphrased the quote.
ReplyDeleteThe first sentence in your second paragraph also caused me some trouble. Perhaps there are some typos there?
I liked the disadvantages that you identified, and agree that they are somewhat troublesome. I wonder, however, about the last disadvantage, namely the inability to guarantee that every student is learning. Is there really an instructional method that can guarantee this? For example, does a focus on learning rules and procedures through direct instruction and ample practice guarantee that every student masters the content? In my own experience trying to teach this way, the answer is definitely no. And even if someone were to successfully pass this type of a course, does that mean he or she really learned mathematics? Or is it possible that the person was a cleverer version of Benny? This is a really high standard for any instructional method. Maybe a more appropriate question to ask would be whether a particular instructional method is better than others at helping more students learn mathematics.
I think it's really important that you are asking questions like that. I wonder though if any method of teaching can really appeal to every student. My dad told me once (he's an auto-mechanic teacher)that he has to do many different things and try many different things because everyone is different and not one way will work for everyone.
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